US House of Representatives - Committee Memberships by Party

The paper from the Congressional Research Service: House Committee Party Ratios: 98^th-116^th Congresses tells us that how the majority and minority parties in Congress divvy up committee seats is rather opaque.

The Standing Rules of the House of Representatives are silent regarding committee sizes and party ratios; the apportionment of committee seats is a decision of the majority leadership that may include discussions between majority and minority party leaderships.  

Only in the House Committee on Ethics are the two parties guaranteed by House Rules to have an equal share of seats. 

Historically, the number of majority seats on some committees has exceeded, in varying degrees, the strength of the majority party in the House chamber, regardless of which party has been in power.  This generally has ensured that the majority party has a sufficient number of members distributed across committees to control voting in many committees.

Based on Table 1 in the paper, the following chart can be drawn. The x-axis is the fraction of House seats the majority holds; the y-axis is the fraction of committee seats the majority holds. Note that the origin is (50,52) (so that you aren't inadvertantly misled by statistics, it is good practice to point that out). In the 117^th Congress, as of January 15^th the Democrats have 221 seats, the Republicans 211. This translates to a 51.2% majority and that translates to a predicted 54.1% of the committee seats.