After reading this thread i wanted to start a little sandbox test.
1. Start a 1936 campaign with SCH, delete all units and save on 1.1.1939. SCH has 27 provinces.
2. Edit savegame:
a) Start two wars. GER against SCH and ITA against SCH
b) Change the capital Basel to 0 VP.
c) Change two SCH provinces to 1 VP. So we have 3 single VP in switzerland.
d) Change one SCH province to 5 VP. (for proofing if VP count as "base provinces")
e) Change NU of SCH to 10
3. Load savegame as Germany.
Now the test starts (between every test, i load the savegame):
1.) Giving Germany only one of the 1VP provinces.
-> SCH surrenders to GER
2.) Giving Italy only one of the 1VP provinces
-> SCH surrenders to ITA
3.) Giving Italy only one of the 1VP provinces and Germany one non VP province
-> SCH surrenders to GERMANY????? Germany gets Switzerland. Italy gets the single VP province.
4.) Giving Italy one 1VP province and one no VP province. Germany gets one non VP province.
-> SCH surrenders to Germany... again?
Being confused, I now LOAD UP AS FRANCE (maybe it is because i am the player that makes Germany get SCH):
1.) Giving Germany only one of the 1VP provinces.
-> SCH surrenders to GER
2.) Giving Italy only one of the 1VP provinces
-> SCH surrenders to ITA
3.) Giving Italy only one of the 1VP provinces and Germany one non VP province
-> SCH surrenders to Germany. Germany gets Switzerland. Italy gets the single VP province.
4.) Giving Germany only one of the 1VP provinces and Italy one non VP province.
->SCH surrenders to Germany.
5.) Giving ITA two 1VP provinces and Germany one non VP province.
-> SCH surrenders to Germany
6.) Giving ITA everything but one province, which goes to germany.
-> SCH surrenders to Italy. Ok good... it was getting frustrating.
7.) Giving ITA everything but the capital and one province. This province but not the capital goes to Germany.
-> SCH surrenders to Italy.
8.) Giving ITA everything but the capital and x provinces. These X provinces with 0 VP will go to Germany. X will be the number of provinces which will lead to a surrender to Germany. The capital is always controlled by SCH.
-> With Germany having 16 or more provinces, SCH surrenders to them. Germany has no VP conquered. ITA has 4 VP provinces with a total of 8VP and 6 non VP provinces. I repeated this 10 times. 5 times with Germany holding 15 and 5 times them holding 16.
9.) Giving Germany 15 non VP provinces and reducing the Vp value of the italian provinces step by step to 1 doesn't make any difference:
-> SCH surrenders to Italy.
10.) Giving Germany 14 non VP provinces and the last VP province, leaving Italy with 11 non VP provinces:
-> SCH surrenders to Italy.
The thread of both to SCH was always 0.000.
The Conclusion: I really don't know. At least we now know that you don't need VP controlled to be the one they surrender to. How many VPs nor how many VP provinces you control doesn't change anything.
EDIT:
I did some further testing, this time involving the capital:
11.) Giving Germany the SCH capital and switching one german controlled province into SCH controlled, so we still have 15 german non VP provinces and 11 italien ones.
-> Now SCH surrenders to Germany. -> the capital makes a difference.
12.) Giving Germany the SCH capital and Italy beside their 11 provinces the SCH controlled non VP province:
-> SCH still surrenders to Germany.
13.) Giving step by step Italy more provinces: With Germany having less than 11 provinces, inclusive the capital and the VP province, and Italy having more than 16 non VP provinces:
-> SCH now surrenders to Italy
14.) Giving Germany 11 provinces, inclusive the capital and the VP province, and Italy having 16 non VP provinces:
-> SCH surrenders to Germany.
15.) Giving Germany 11 provinces, inclusive the capital and Italy 16 provinces, inclusive the VP province:
->SCH still surrenders to Germany. VPs really don't change anything.
So the Capital really makes some huge difference.
BTW: It doesn't matter if the conquered provinces are connected to the main land of the conquerer. cutting of german controlled Basel from the german main land and with still 11 german and 16 italian provinces, SCH still surrenders to Germany.