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Trying to find out who signatures is on this Basebball . I received it as a birthday present
This is a David Ortiz autograph. "B.P." almost certainly stands for "Big Papi", Ortiz's very common nickname.
There are many examples. Here is his Baseball Almanac page.
Exhibit A (last card on page):
Exhibit B (note the 34 in the signature):
2 years ago
11 months ago