Can I take the full capital commitment from an LP at the first close? What if I expect 10% of the Fund's LPs to come in at the first close? Does that change anything?

Generally speaking, no - if an LP commits $100K, then on the first close, whatever percentage the capital call is for (typically 20% or 25%) should be wired by the limited partner. For example, an LP that has committed $100K to the fund receives a first close capital call notice for 20% of the LP's committed capital - so the LP wires $20K. The LP should generally not wire more than $20K, as this introduces additional accounting complexities - even if the LP were to so, the additional capital would not be able to be deployed.

Decile Partners and VC Lab strongly recommend waiting until a fund has at least 10% of the target fund size committed to begin a first close - however this percentage is not the same as the capital call percentage.

Please read the following regarding capital calls:

https://govclab.com/2023/05/07/vc-capital-calls/